Stone Coalgebras

  title={Stone Coalgebras},
  author={Clemens Kupke and Alexander Kurz and Yde Venema},
  journal={Theor. Comput. Sci.},
Algebraic Semantics for Coalgebraic Logics
Strongly Complete Logics for Coalgebras
A general construction of a logic from an arbitrary set-functor is given and proven to be strongly complete under additional assumptions and it is argued that sifted colimit preserving functors are those functors that preserve universal algebraic structure.
Coalgebraic Geometric Logic: Basic Theory
Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an
Completeness for the coalgebraic cover modality
A derivation system is introduced, and it is proved that it provides a sound and complete axiomatization for the collection of coalgebraically valid inequalities, and the Lindenbaum-Tarski algebra of the logic can be identified with the initial algebra for this functor.
Duality for powerset coalgebras
Thomason duality is derive from Tarski duality, thus paralleling how Jónsson-TarskiDuality is derived from Stone duality.
A Coalgebraic Approach to Dualities for Neighborhood Frames
An endofunctor is constructed on the category of complete and atomic Boolean algebras that is dual to the double powerset functor on Set to show that Thomason duality for neighborhood frames can be viewed as an algebra-coalgebra duality.
Coalgebraic Geometric Logic
Using the theory of coalgebra, a uniform framework for adding modalities to the language of propositional geometric logic is introduced, and a method of lifting an endofunctor on $\mathbf{Set}$, accompanied by a collection of predicate liftings, to an end ofunctors on the category of topological spaces.
Enriched Stone-type dualities
Ultrafilter Extensions for Coalgebras
The Jonsson-Tarski theorem giving a set-theoretic representation for each modal algebra and the bisimulation-somewhere-else theorem stating that two states of a coalgebra have the same (finitary modal) theory iff they are bisimilar (or behaviourally equivalent) in the ultrafilter extension of the coalgebra are generalised.
Presenting Functors by Operations and Equations
A result is obtained that allows us to prove adequateness of logics uniformly for a large number of different types of transition systems and give some examples of its usefulness.


A study of categories of algebras and coalgebras
This thesis is intended to help develop the theory of coalgebras by, first, taking classic theorems in the theory of universal algebras and dualizing them and, second, developing an internal logic
Coalgebraic modal logic of finite rank
The notion of finiteStep equivalence and a corresponding category with finite step equivalence-preserving morphisms always has a final object, which generalises the canonical model construction from Kripke models to coalgebras.
A Coalgebraic View of Heyting Duality
The category of Heyting spaces is isomorphic to a full subcategory of the category of all Γ-coalgebras, based on Boolean spaces, where Γ is the functor which maps a Boolean space to its hyperspace of nonempty closed subsets.
Coalgebraic Logic
  • L. Moss
  • Mathematics
    Ann. Pure Appl. Log.
  • 1999
Universal coalgebra: a theory of systems
A Cook's Tour of the Finitary Non-Well-Founded Sets
A topological universe of finitary sets, which can be seen as a natural limit completion of the hereditarily finite sets, is given, which contains non-well founded sets and a universal set and is closed under positive versions of the usual axioms of set theory.
Coalgebras and Modal Logic